Let \(\xi :E\rightarrow B\)  be a smooth bundle with a connection, and let \(\Omega \)  be the associated curvature form. Classical Chern-Weil theory (cf. §5.4 in [1]})) says that the total Pontrjagin class of \(E\)  with coefficients in \({\mathbb {R}}\)  is
\(P(E)=\sum _i p_i(E)=\left[\det \left( I +\frac{1}{2\pi }\Omega \right)\right]\) 
